Skis or the like of this type have a runner base top layer with a first outer surface, two steel edge profiles mounted on two longitudinal edges, each with a second outer surface facing downwards when in use and a third outer surface facing laterally. Steel edges of this type are found predominantly on skis but also on skate runners or the like. Whether the steel edges are sharp and remain sharp determines to a large extent the properties of skis. Sharp steel edges afford good guide properties, in particular on ice. The runner top layer on skis is plastic. Its outer surface must essentially coincide with the outer surface of the steel edges parallel to it, and that is why the steel edge profile of a ski blank having a runner base and steel edges is ground down until it has the desired height relative to the outer surface of the runner base top layer. In order to facilitate this working down, relatively soft steel edge profiles are used, for example with a value of Rc48. A relatively rapid blunting of the steel edge profiles is consequently accepted.